Three-dimensional CP-DNS of reacting iron particle dust clouds in a turbulent mixing layer are conducted. The simulation approach considers the Eulerian transport equations for the reacting gas phase and resolves all scales of turbulence, whereas the particle boundary layers are modelled employing the Lagrangian point-particle framework for the dispersed phase. The CP-DNS employs an existing sub-model for iron particle combustion that considers the oxidation of iron to FeO and that accounts for both diffusion- and kinetically-limited combustion. At first, the particle sub-model is validated against experimental results for single iron particle combustion considering various particle diameters and ambient oxygen concentrations. Subsequently, the CP-DNS approach is employed to predict iron particle cloud ignition and combustion in a turbulent mixing layer. The upper stream of the mixing layer is initialised with cold particles in air, while the lower stream consists of hot air flowing in the opposite direction. Simulation results show that turbulent mixing induces heating, ignition and combustion of the iron particles. Significant increases in gas temperature and oxygen consumption occur mainly in regions where clusters of iron particles are formed. Over the course of the oxidation, the particles are subjected to different rate-limiting processes. While initially particle oxidation is kinetically-limited it becomes diffusion-limited for higher particle temperatures and peak particle temperatures are observed near the fully-oxidised particle state. Comparing the present non-volatile iron dust flames to general trends in volatile-containing solid fuel flames, non-vanishing particles at late simulation times and a stronger limiting effect of the local oxygen concentration on particle conversion is found for the present iron dust flames in shear-driven turbulence.

Classical rupture is attributed to molecular (van der Waals) forces acting at nanometric thicknesses. Nonetheless, micron-thick liquid sheets routinely perforate far above the scale where these molecular forces act, yet the mechanism that selects opening versus healing has remained unclear. Using direct numerical simulations of a draining sheet with an entrained air bubble (cavity), we show that irreversible rupture occurs only when a deterministic double-threshold is crossed: (i) the outward driving (from airflow or inertia) is strong enough and (ii) the cavity is distorted enough. If either condition falls short, surface tension heals the cavity and the sheet reseals. The time for this process is set by the balance between inertia and viscosity -- fast for inertia-dominated sheets and slower for viscous ones. This double-threshold mechanism explains why micrometer-thick films perforate and offers practical control options -- driving strength and defect geometry -- for predicting and controlling breakup in spray formation processes, wave breaking, and respiratory films.

The growth, lifetime, number density, and size of water droplets in warm atmospheric clouds determine the evolution, lifetime and light transmission properties of those clouds. These small-scale cloud properties, in addition to precipitation initiation, have strong implications for the Earth's energy budget since warm clouds cover large geographic areas. Spatio-temporal correlations on the millimetre scale and smaller may or may not affect these properties of clouds. To date, the pioneering measurements of such correlations in marine stratocumulus clouds have relied on averaging over holographically reconstructed volumes spanning at least ten kilometres. These have revealed weak but widespread spatial clustering of cloud droplets. Here we present results of strong localised clustering on scales of half a metre or less from holographic measurements collected with the Max Planck CloudKite in shallow cumulus clouds in the mid-Atlantic trade wind region near Barbados, with a spatial separation of only 12~cm between measurement volumes. This observation challenges the foundations of our understanding of cloud microphysics at the droplet scale, with implications for cloud modelling in weather and climate prediction.

Phase separation is the thermodynamic process that explains how droplets form in multicomponent fluids. These droplets can provide controlled compartments to localize chemical reactions, and reactions can also affect the droplets' dynamics. This review focuses on the tight interplay between phase separation and chemical reactions originating from thermodynamic constraints. In particular, simple mass action kinetics cannot describe chemical reactions since phase separation requires non-ideal fluids. Instead, thermodynamics implies that passive chemical reactions reduce the complexity of phase diagrams and provide only limited control over the system's behavior. However, driven chemical reactions, which use external energy input to create spatial fluxes, can circumvent thermodynamic constraints. Such active systems can suppress the typical droplet coarsening, control droplet size, and localize droplets. This review provides an extensible framework for describing active chemical reactions in phase separating systems, which forms a basis for improving control in technical applications and understanding self-organized structures in biological cells.

The decay of Taylor-Couette turbulence, i.e~the flow between two coaxial and independently rotating cylinders, is numerically studied by instantaneously stopping the forcing from an initially statistically stationary flow field at a Reynolds number of $Re=3.5\times 10^4$. The effect of wall-friction is analysed by comparing three separate cases, in which the cylinders are either suddenly made no-slip or stress-free. Different life stages are observed during the decay. In the first stage, the decay is dominated by large-scale rolls. Counterintuitively, when these rolls fade away, if the flow inertia is small a redistribution of energy occurs, the energy of the azimuthal velocity behaves non-monotonically: first decreasing by almost two orders of magnitude, and then increasing during the redistribution. The second stage is dominated by non-normal transient growth of perturbations in the axial (spanwise) direction. Once this mechanism is exhausted, the flow enters the final life stage, viscous decay, which is dominated by wall-friction. We show that this stage can be modeled by a one-dimensional heat equation, and that self-similar velocity profiles collapse onto the theoretical solution.

We experimentally investigated the melting of floating ice cylinders. Experiments were carried out in an aquarium, with ice cylinders with radii between 5 cm and 12 cm, floating horizontally with their axis perpendicular to gravity. The water in the aquarium was at room temperature, with salinities ranging from 0 g/L to 35 g/L. These conditions correspond to Rayleigh numbers in the range 10^5 <= Ra <= 10^9. The relative density and thus the floating behaviour could be varied by employing ice made of H2O-D2O mixtures. In addition, we explored a two-layer stable stratification. We studied the morphological evolution of the cross section of the cylinders, and explained it through the interaction with the convective flow. The cylinders only capsize in fresh water but not when the ambient is saline. This behaviour can be explained using geometrical arguments. We modelled the oscillatory motion of the cylinders after a capsize as a damped non-linear oscillator. The downward plume of the ice cylinders follows the expected scalings for a line-source plume. The plume's Reynolds number scales with Rayleigh number in two regimes, namely Re scales as Ra^1/2 for Ra < O(10^7) and Re scales as Ra^1/3 for Ra > O(10^7), and the heat transfer (nondimensional as Nusselt number) scales as Nu scales as Ra^1/3. These scaling relations hold irrespectively of the initial size or the water salinity. Our results can qualitatively be connected to natural phenomena occurring in fjords and around isolated icebergs.

A sequence of two and three-dimensional simulations is conducted for the double diffusive convection (DDC) flows in the diffusive regime subjected to an imposed shear. The flow is confined between two horizontal plates which are maintained at different constant temperature, salinity, and different velocity, thus setting up a shear across the flow. The lower plate is fixed at higher temperature and salinity, while the overall (unperturbed) density gradient is statically stable. For a wide range of control parameters, and for sufficiently strong perturbation of the conductive initial state, we find that staircase-like structures spontaneously develop, with relatively well-mixed layers separated by sharp interfaces of enhanced scalar gradient. Such staircases appear to be robust even in the presence of strong shear over very long times, although we typically observe early time coarsening of the number of observed layers. For the same set of control parameters, different asymptotic layered states, with markedly different vertical scalar fluxes, can arise for different initial perturbation structures. The imposed shear does significantly spatio-temporally modify the vertical transport of the various scalars. The flux ratio (i.e., the ratio between the density fluxes due to the total (convective and diffusive) salt flux and the total heat flux) is found, at steady state, to be essentially equal to the square root of the ratio of the salt diffusivity to the thermal diffusivity, consistently with the physical model originally proposed by Linden and Shirtcliffe (1978) and the variational arguments presented by Stern (1982) for unsheared double diffusive convection.

We conduct two- and three-dimensional simulations for double diffusive convection in the diffusive regime, where the fluid flow is driven by a destabilizing temperature gradient and stabilized by a stably stratified salinity gradient. We study how the heat flux, Reynolds number, and flow structures change with the density ratio $\Lambda$, which is the ratio of the buoyancy force induced by the salinity gradient to that by the temperature gradient. When $\Lambda$ increases from zero, the flow first behaves similarly as in pure Rayleigh-B\'enard (RB) convection, both with respect to flow structure and to heat transport. The linear stability analysis of Baines & Gill (J. Fluid Mech., vol. 37, 1969, pp. 289-306) had estimated the critical density ratio $\Lambda_c$, above which the flow becomes stable. However, here we show that by using a large-scale circulation as initial condition (rather than the linear profiles assumed in the linear stability analysis), DDC in the diffusive regime can exhibit subcritical behaviour when $\Lambda > \Lambda_c$, i.e., coexistence of states at the same control parameters. Even though the density ratio becomes thousands times that of the critical value $\Lambda_c$, there is still convection with strongly enhanced heat transfer properties compared to the pure conduction case. We reveal the corresponding flow structures and find an unstably-stratified region sandwiched between two stably-stratified layers. Our results demonstrate the importance of the initial condition for DDC in the diffusive regime, especially in the situation of a large density ratio, which occurs in high-latitude ocean regions.

Accurate numerical modeling of surface tension has been a challenging aspect of multiphase flow simulations. The integral formulation for modeling surface tension forces is known to be consistent and conservative, and to be a natural choice for the simulation of flows driven by surface tension gradients along the interface. This formulation was introduced by Popinet and Zaleski (1999) for a front-tracking method and was later extended to level set methods by Al-Saud et al. (2018). In this work, we extend the integral formulation to a volume of fluid (VOF) method for capturing the interface. In fact, we propose three different schemes distinguished by the way we calculate the geometric properties of the interface, namely curvature, tangent vector and surface fraction from VOF representation. We propose a coupled level set volume of fluid (CLSVOF) method in which we use a signed distance function coupled with VOF, a height function (HF) method in which we use the height functions calculated from VOF, and a height function to distance (HF2D) method in which we use a sign-distance function calculated from height functions. For validation, these methods are rigorously tested for several problems with constant as well as varying surface tension. It is found that from an accuracy standpoint, CLSVOF has the least numerical oscillations followed by HF2D and then HF. However, from a computational speed point of view, HF method is the fastest followed by HF2D and then CLSVOF. Therefore, the HF2D method is a good compromise between speed and accuracy for obtaining faster and correct results.

Bubble coalescence can promote bubble departure at much smaller sizes compared to buoyancy. This can critically enhance the efficiency of gas-evolving electrochemical processes, such as water electrolysis. In this study, we integrate high-speed imaging experiments and direct numerical simulations to dissect how and under which conditions bubble coalescence on surfaces leads to detachment. Our transparent electrode experiments provide new insights into contact line dynamics, demonstrating that the bubble neck generally does not contact the surface during coalescence. We reveal that whether coalescence leads to bubble departure or not is determined by the balance between surface energy, adhesion forces, and viscous dissipation. For the previously unexplored regime at low effective Ohnesorge number, a measure of viscosity that incorporates the effect of asymmetry between the coalescing bubbles, we identify a critical dimensionless adhesion energy threshold of $\approx$15% of the released surface energy, below which bubbles typically detach. We develop a global energy balance model that successfully predicts coalescence outcomes across diverse experimental conditions.

Biological flow networks adapt their network morphology to optimise flow while being exposed to external stimuli from different spatial locations in their environment. These adaptive flow networks retain a memory of the stimulus location in the network morphology. Yet, what limits this memory and how many stimuli can be stored is unknown. Here, we study a numerical model of adaptive flow networks by applying multiple stimuli subsequently. We find strong memory signals for stimuli imprinted for a long time into young networks. Consequently, networks can store many stimuli for intermediate stimulus duration, which balance imprinting and ageing.

Using volumetric velocity data from a turbulent laboratory water flow and numerical simulations of homogeneous, isotropic turbulence, we present a direct experimental and numerical assessment of Kolmogorov's first refined similarity hypothesis based on three-dimensional measurements of the local energy dissipation rate $\epsilon_r$ measured at dissipative scales $r$. We focus on the properties of the stochastic variables $V_L = \Delta u(r)/(r \epsilon_r)^{1/3}$ and $V_T = \Delta v(r)/(r\epsilon_r)^{1/3}$, where $\Delta u(r)$ and $\Delta v(r)$ are longitudinal and transverse velocity increments. Over one order of magnitude of scales $r$ within the dissipative range, the distributions of $V_L$ and $V_T$ from both experiment and simulation collapse when parameterised by a suitably defined local Reynolds number, providing the first conclusive experimental evidence in support of the first refined similarity hypothesis and its universality.

We experimentally investigate the evaporation of very volatile liquid droplets (Novec 7000 Engineered Fluid) in a turbulent spray. Droplets with diameters of the order of a few micrometers are produced by a spray nozzle and then injected into a purpose-built enclosed dodecahedral chamber, where the ambient temperature and relative humidity in the chamber are carefully controlled. We observe water condensation on the rapidly evaporating droplet, both for the spray and for a single acoustically levitated millimetric Novec 7000 droplet. We further examine the effect of humidity, and reveal that a more humid environment leads to faster evaporation of the volatile liquid, as well as more water condensation. This is explained by the much larger latent heat of water. We extend an analytical model based on Fick's law to quantitatively account for the data.

The critical state is assumed to be optimal for any computation in recurrent neural networks, because criticality maximizes a number of abstract computational properties. We challenge this assumption by evaluating the performance of a spiking recurrent neural network on a set of tasks of varying complexity at - and away from critical network dynamics. To that end, we developed a spiking network with synaptic plasticity on a neuromorphic chip. We show that the distance to criticality can be easily adapted by changing the input strength, and then demonstrate a clear relation between criticality, task-performance and information-theoretic fingerprint. Whereas the information-theoretic measures all show that network capacity is maximal at criticality, this is not the case for performance on specific tasks: Only the complex, memory-intensive tasks profit from criticality, whereas the simple tasks suffer from it. Thereby, we challenge the general assumption that criticality would be beneficial for any task, and provide instead an understanding of how the collective network state should be tuned to task requirement to achieve optimal performance.

The dynamics of drop impact on a rigid surface -- omnipresent in nature and technology -- strongly depends on the droplet's velocity, its size, and its material properties. The main characteristics are the droplet's force exerted on the surface and its maximal spreading radius. The crucial question is: How do they depend on the (dimensionless) control parameters, which are the Weber number $We$ (non-dimensionalized kinetic energy) and the Ohnesorge number $Oh$ (dimensionless viscosity)? Here we perform direct numerical simulations over the huge parameter range $1\le We \le 10^3$ and $10^{-3}\le Oh \le 10^2$ and in particular develop a unifying theoretical approach, which is inspired by the Grossmann-Lohse theory for wall-bounded turbulence [J. Fluid Mech. 407, 27 (2000); PRL 86, 3316 (2001)]. The key idea is to split the energy dissipation rate into the different phases of the impact process, in which different physical mechanisms dominate. The theory can consistently and quantitatively account for the $We$ and $Oh$ dependences of the maximal impact force and the maximal spreading diameter over the huge parameter space. It also clarifies why viscous dissipation plays a significant role during impact, even for low-viscosity droplets (low $Oh$), in contrast to what had been assumed in prior theories.

Streaming Dynamic Mode Decomposition (sDMD) (Hemati et al., Phys. Fluids 26(2014)) is a low-storage version of Dynamic Mode Decomposition (DMD) (Schmid, J. Fluid Mech. 656 (2010)), a data-driven method to extract spatio-temporal flow patterns. Streaming DMD avoids storing the entire data sequence in memory by approximating the dynamic modes through incremental updates with new available data. In this paper, we use sDMD to identify and extract dominant spatio-temporal structures of different turbulent flows, requiring the analysis of large datasets. First, the efficiency and accuracy of sDMD are compared to the classical DMD, using a publicly available test dataset that consists of velocity field snapshots obtained by direct numerical simulation of a wake flow behind a cylinder. Streaming DMD not only reliably reproduces the most important dynamical features of the flow; our calculations also highlight its advantage in terms of the required computational resources. We subsequently use sDMD to analyse three different turbulent flows that all show some degree of large-scale coherence: rapidly rotating Rayleigh--B\'enard convection, horizontal convection and the asymptotic suction boundary layer. Structures of different frequencies and spatial extent can be clearly separated, and the prominent features of the dynamics are captured with just a few dynamic modes. In summary, we demonstrate that sDMD is a powerful tool for the identification of spatio-temporal structures in a wide range of turbulent flows.

When a rising bubble in a Newtonian liquid reaches the liquid-air interface, it can burst, leading to the formation of capillary waves and a jet on the surface. Here, we numerically study this phenomenon in a yield stress fluid. We show how viscoplasticity controls the fate of these capillary waves and their interaction at the bottom of the cavity. Unlike Newtonian liquids, the free surface converges to a non-flat final equilibrium shape once the driving stresses inside the pool fall below the yield stress. Details of the dynamics, including the flow's energy budgets, are discussed. The work culminates in a regime map with four main regimes with different characteristic behaviours.

A falling liquid drop, after impact on a rigid substrate, deforms and spreads, owing to the normal reaction force. Subsequently, if the substrate is non-wetting, the drop retracts and then jumps off. As we show here, not only is the impact itself associated with a distinct peak in the temporal evolution of the normal force, but also the jump-off, which was hitherto unknown. We characterize both peaks and elucidate how they relate to the different stages of the drop impact process. The time at which the second peak appears coincides with the formation of a Worthington jet, emerging through flow-focusing, and it is independent of the impact velocity. However, the magnitude of this peak is dictated by the drop's inertia and surface tension. We show that even low-velocity impacts can lead to a surprisingly high peak in the normal force, namely when a more pronounced singular Worthington jet occurs due to the collapse of an air cavity in the drop.

We present a generalisation of the all-Mach solver of Fuster & Popinet (2018) to account for heat diffusion between two different compressible phases. By solving a two-way coupled system of equations for pressure and temperature, the current code is shown to increase the robustness and accuracy of the solver with respect to classical explicit discretization schemes. Different test cases are proposed to validate the implementation of the thermal effects: an Epstein-Plesset like problem for temperature is shown to compare well with a spectral method solution. The code also reproduces free small amplitude oscillations of a spherical bubble where analytical solutions capturing the transition between isothermal and adiabatic regimes are available. We show results of a single sonoluminescent bubble (SBSL) in standing waves, where the result of the DNS is compared with that of other methods in the literature. Moreover, the Rayleigh collapse problem is studied in order to evaluate the importance of thermal effects on the peak pressures reached during the collapse of spherical bubbles. Finally, the collapse of a bubble near a rigid boundary is studied reporting the change of heat flux as a function of the stand-off distance.